Read Birth of a Theorem: A Mathematical Adventure Online

Authors: Cédric Villani

Tags: #Non-Fiction, #Science, #Biography

Birth of a Theorem: A Mathematical Adventure (23 page)

BOOK: Birth of a Theorem: A Mathematical Adventure
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Let
with
0
<
λ
*
<
λ
0
.
Let
be a continuous function of t
≥
0,
valued in
such that

(7.22)

 

where c
0
≥
0
, m
>
1
,
and
K
0
(
t,
τ)
, K
1
(
t,
τ)
are nonnegative kernels. Let
Then

(i) Assume
γ
>
1
and K
1
=
cK
(
α
),
γ
for some c
>
0,
where
K
(
α
),
γ
is defined by

 

and
appears in Proposition 7.1. Then there are positive constants C and
χ
,
depending only on
γ,
λ
*,
λ
0
,
κ
,
c
0
,
C
W
,
m, uniform as
γ
→
1
, such that if

(7.23)

 

and

(7.24)

 

then for any

BOOK: Birth of a Theorem: A Mathematical Adventure
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